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The semicircle shown at left has center X XX and diameter W Z ‾ ​WZ ​ ​​ start overline, W, Z, end overline. The radius X Y ‾ ​XY ​ ​​ start overline, X, Y, end overline of the semicircle has length 2 22. The chord Y Z ‾ ​YZ ​ ​​ start overline, Y, Z, end overline has length 2 22. What is the area of the shaded sector formed by obtuse angle W X Y WXYW, X, Y?

Respuesta :

sqdancefan
Triangle XYZ is equilateral, so the central angle of the sector is 120°, or 2π/3 radians. The area of a sector of central angle β is given by
.. A = (1/2)r^2*β . . . . . . β in radians
Your sector's area is
.. A = (1/2)*2^2*(2π/3) = 4π/3 . . . . square units

The area of the shaded region is 4π/3 square units.

We have given that x= center diameter =wz w and z end over line radius=2

Triangle XYZ is equilateral,

What is the central angle of equilateral ?

120 degrees

so the central angle of the sector is 120°,

In radian

=120×[tex]\pi[/tex]/180

=2π/3 radians.

The area of a sector of central angle β is given by,

[tex]A = (1/2)r^2(\beta )[/tex] . . . . . . β in radians

[tex]A = (1/2)*2^2*(2\pi /3)[/tex]    

 = 4π/3 . . . . square units

Therefore the area of the shaded region is 4π/3 square units.

To learn more about equilateral tingle area visit:

https://brainly.com/question/1099318

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